4.5 Article

Properties of the scattering matrix and dispersion estimates for Jacobi operators

Journal

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 434, Issue 1, Pages 956-966

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2015.09.047

Keywords

Jacobi operator; Dispersive estimates; Scattering; Resonant case

Funding

  1. Department of Mathematics at the University of Vienna
  2. Austrian Science Fund (FWF) [W1245, V120] Funding Source: Austrian Science Fund (FWF)

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We show that for a Jacobi operator with coefficients whose (j + 1)'th moments are summable the j'th derivative of the scattering matrix is in the Wiener algebra of functions with summable Fourier coefficients. We use this result to improve the known dispersive estimates with integrable time decay for the time dependent Jacobi equation in the resonant case. (C) 2015 Elsevier Inc. All rights reserved.

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